optimization?

Question

It is estimated that t years from now the population of a certain country will be
P(t) = 50/(1+6 e^(- 0.04 t))
million. When will the population be growing most rapidly?

In order to solve the problem, you have to maximize the function R(t) that gives the growth rate of the population, i.e. R(t)=P'(t). Check that
R(t)= (12 e^(- 0.04 t))/((1+6 e^(- 0.04 t))^2).

Now you need the critical numbers of the rate function. Check that

R'(t)= (0.48 e^(- 0.04 t))(6 e^{- 0.04 t}-1))/((1+6 e^(- 0.04 t))^3).
and use it to find the critical number that corresponds to the maximal rate t

WHAT DOES T= ?????

Answer 1

t is the time value that makes R'(t) = 0

Are you asking us to do the computation for you?